Re-runs made when the note was written (2026-10-20). Each program was run in place, with its output
redirected to a new file outside the package, and compared byte by byte (cmp) with the recorded output. Python 3.13.5; SymPy 1.14.0; NumPy 2.5.2; SciPy 1.18.1.

check_note.py                          0.04 s   33 of 33 PASS   output identical to check_note_output.txt
original/check_conjugation.py          0.24 s   all True        output identical to check_conjugation_output.txt
verification_run_A/my_check.py         0.22 s   all True        output identical to my_check_output.txt
verification_run_B/vb_symbolic.py      0.88 s   as expected     output identical to vb_symbolic_output.txt
verification_run_B/vb_ccdist.py       10.30 s   (illustration)  output identical to vb_ccdist_output.txt

Negative control of check_note.py (not part of the package): sigma replaced by diag(1, -1, 1, 1), tau by
(x, -y, t), A by (2x, y, t): 7 checks FAIL (sigma anticommutes with J0; d sigma maps H onto H; sigma^* theta =
-theta; det sigma = 1; the two tau checks; the A check), 26 PASS, final line "SOME CHECKS FAILED".

Re-run of the final package (2026-10-20, after the corrections of verification run 2). The source archive was
built, extracted into an empty folder, and each program run there with 'python -I -B <program>', the output
redirected to a new file and compared byte by byte (cmp) with the recorded output. Python 3.13.5; SymPy 1.14.0;
NumPy 2.5.2; SciPy 1.18.1.

check_note.py                          0.04 s   33 of 33 PASS   output identical to check_note_output.txt
original/check_conjugation.py          0.66 s   all True        output identical to check_conjugation_output.txt
verification_run_A/my_check.py         0.24 s   all True        output identical to my_check_output.txt
verification_run_B/vb_symbolic.py      0.95 s   as expected     output identical to vb_symbolic_output.txt
verification_run_B/vb_ccdist.py        3.84 s   (illustration)  output identical to vb_ccdist_output.txt
independent_run_2/run2_certificate.py  1.49 s   36 of 36 PASS   output identical to run2_certificate_output.txt
No __pycache__ folder was created.
